Using the well-known dynamic fiscal policy framework pioneered by Auerbach and Kotlikoff, we examine the efficiency and welfare implications of shifting from a linear marginal tax rate structure to a discrete rate structure characterized by two regions of flat tax rates of 15 and 28 percent. For a wide range of parameter values, we find that there is no sequence of lump-sum transfers that the (model) government can feasibly implement to make the shift from the linear to the discrete structure Pareto-improving. We conclude that the worldwide trend toward replacing rate structures having many small steps between tax rates with structures characterized by just a few large jumps is not easily accounted for by efficiency arguments. In the process of our analysis, we introduce a simple algorithm for solving dynamic fiscal policy models that include "kinks" in individual budget surfaces due to discrete tax codes. In addition to providing a relatively straightforward way of extending Auerbach-Kotlikoff-type models to this class of problems, our approach has the side benefit of facilitating the interpretation of our results.